To develop this problem it is necessary to apply the concepts related to Gravitational Potential Energy.
Gravitational potential energy can be defined as

As M=m, then

Where,
m = Mass
G =Gravitational Universal Constant
R = Distance /Radius
PART A) As half its initial value is u'=2u, then



Therefore replacing we have that,

Re-arrange to find v,



Therefore the velocity when the separation has decreased to one-half its initial value is 816m/s
PART B) With a final separation distance of 2r, we have that

Therefore




Therefore the velocity when they are about to collide is 
Answer:
a) d = 6.0 m
Explanation:
Since car is accelerating at uniform rate then here we can say that the distance moved by the car with uniform acceleration is given as

here we know that



now we will have



Answer:
generators
Explanation:
the machine which turns in a power station
Answer:
The frequency of sound heard by the boy is 1181 Hz.
Explanation:
Given that,
Frequency of sound from alarm 
Speed = -8.25 m/s
Negative sign show the boy riding away from the car
Speed of sound = 343
We need to calculate the heard frequency
Using formula of frequency

Where,
= frequency of source
= speed of observer
= speed of source
= speed of sound
Put the value into the formula

here, source is at rest


Hence, The frequency of sound heard by the boy is 1181 Hz.
Wildlife researcher starts from a and then reaches b, he turns towards north 40 degree to move towards c.
Total displacement is ac
Total horizontal displacement = 4+4 cos40 =7.06 km
Total vertical displacement = 4 sin40 =2.57 km
Total displacement
= 7.51 km